Why saddened? ... I admit i don't know economics at all :-(

Because of what it says about economics -- that an outsider can reach the same conclusion, for the same reason, as (half of) the "experts". Remember the "layshadow test"? If an academic field is such that a layperson can come in, spend a few hours, and produce output indistinguishable from people who have spent years "learning" the field, then that field is lost because the inferential distance is low, implying little knowledge accumulation.

That's what seems to be going on here.

And what is the other side's standard response to my (apparently well-known) question?

I just found out there's a Wikipedia article about the debate. It doesn't give the response to that critique, but as far as I know, the response is that it requires flexible prices throughout the economy and won't work if prices are "sticky".

Correction: Here's another critique from there:

Mitchell criticizes this because, he asserts, the falling wages of babysitters only solves the problem if it reduces the desire of couples to save, which is not supported by any research.[9] The only effect of falling wages would be to increase the real value of nominal contracts. In other words, couples would have to spend more time babysitting before they acquired the amount necessary to leave the cooperative. Mitchell concludes that the problem is greater aggregate desire to save than can be funded by existing administrative debt, and that the solution is thus either to reduce (desire for) savings or, more likely increase spending by simply issuing more scrip.